Cambridge: all you need to know

It may be crammed with boffins and bookworms, but this city of swooning poets and weeping willows appeals to the heart as much as the head, says resident E Jane Dickson

An asylum, in every sense of the word.' That was AE Housman's pronouncement on Cambridge. Maybe not the ideal marketing slogan, but oddly accurate. The university city, for centuries the crucible of rational thought and cultured eccentricity, rises like a lovely hallucination from the Fens. In its medieval lanes, loud with the whirr of bicycle wheels, mad-eyed mathematicians lock handlebars with floaty girls where Newton and Plath once strayed. Cattle graze on unexpected urban pasture. And the newest landmark, a monumental clock erected by Corpus Christi College in 2008 to mark the 800th anniversary of the university, confirms the peculiar spirit of the place. A giant mechanical grasshopper biting chunks out of time, the 'Chronophage' reflects Einstein's ideas on the relativity of experience. This marvellous timepiece cost £1 million. Its construction involved 200 people and six newly patented inventions. And it is accurate once every five minutes, which is - literally - academic, because it is by no means clear how you are supposed to read the hour. But that's Cambridge for you. And as Housman also promised, there is no better retreat from a jangling world. There is peace in its quiet courts, glad young life on its wide green spaces. On a spring day smelling of lilac, you may be moved to knock out a sonnet or crack quark theory (really, how hard can it be?). And the tea shops aren't bad, either.

Smart hotel with a panoramic roof terrace Shoe-horned into a narrow passageway moments from Magdalene Bridge, TheVarsity Hotel & Spa has the feeling of a private club. The project of four Cambridge alumni, it's a discreet new-build, bedded into its surroundings using reclaimed materials. Decanters of sherry and portraits of distinguished graduates nod to the Senior Common Room, but rooms are bright and boutiquey. The restaurant, oddly, is around the corner on the riverbank. Planning regulations ruled out direct access from the hotel, but room service goes the extra mile. Ask for a room on the upper storeys, where floor-to-ceiling windows are filled with the city's romantic roofscape. Best of all, the roof-garden bar has a 360-degree gargoyle's view of surrounding colleges. You can peer nosily into cloisters or get your bearings from the annotated watercolour that comes with the drinks list. There's a barbecue brunch up here at weekends. The Varsity Hotel & Spa, Thompson's Lane, Cambridge, England (+44 1223 306030; www.thevarsityhotel.com). Doubles from £165

Stylish bed-and-breakfast in a great locationDuke House, right on the edge of Christ's Pieces, is a very superior B&B with four elegant guest rooms. Owners Liz and Rob Cameron offer a friendly concierge service and the incalculable advantage of free, secure parking. (Cambridge is probably Britain's least car-friendly city; a parking ticket, according to local report, is marginally cheaper than an all-day stay in its most central car park.) Duke House, 1 Victoria Street, Cambridge, England (+44 1223 314773; www.dukehousecambridge.co.uk). Doubles from £130

Top-notch townhouse About 15 miles across the Fens, in Ely, is Poets House, a new hotel and restaurant that has earned an excellent reputation since opening in April. It's a stylishly appointed townhouse opposite Ely Cathedral (check out the austerely beautiful Lady Chapel and its mad, Disney-princess Madonna). Rooms are smart and comfy, with glamorous copper bathtubs, and the pretty garden is a draw for Sunday lunch. Poets House, 40 St Mary's Street, Ely, England (+44 1353 887777; www.poetshouse.com). Doubles from £179

Ten courses, two Michelin starsMidsummer House, in a prime position on the banks of the Cam, is the restaurant of choice for graduation dinners - but every meal here is a celebration. Its two Michelin stars are evident in chef Daniel Clifford's classically based cooking with a witty, English edge. The 10-course tasting menu is a kind of culinary carnival, with larky amuse-bouches (the house Bloody Mary is tomato-vodka foam with celery sorbet) and big-guns mains. Doughnuts served as petits fours are sheer bravado. The wine list stretches from very decent reds and whites around the £35 mark to vintage Krug and Montrachet grands crus beyond the dreams of avarice. Watch proud parents reapply 'it only happens once' smiles when the bill arrives. Midsummer House, Midsummer Common, Cambridge, England (+44 1223 369299; www.midsummerhouse.co.uk). Ten-course tasting menu £95

Sensational Sicilian picnic treats For refuelling on the hoof, follow your nose to Aromi, where yard-long flatbreads are pulled from wood-burning ovens. Recently opened behind the Guildhall, this is an authentic Sicilian pizzeria with ingredients imported on a weekly basis. Pillowy schiacciatelle, stuffed with pancetta, caciotta cheese, artichokes and handmade arancini (risotto balls that are perfect for a riverside picnic), are served at warp speed by shouty Italians. If you can shoulder your way to one of the tiny tables inside, the coffee and doll-sized pastries are outstanding. Aromi, 1 Bene't Street, Cambridge, England (+44 1223 300117; www.aromi.co.uk)

Revamped café for foodiesFitzbillies is a much-loved Cambridge institution, famous for sticky buns made to the same recipe since 1922. The tea shop, a hats-and-cakestands, EM Forster kind of place, was saved from the receiver in 2011 by food writer Tim Hayward. It is now open daily for coffee, cakes and lunch, and from Thursday to Saturday for dinner: the seasonal menu might include lamb rump, spiced aubergine or roast hake. Fitzbillies, 51-52 Trumpington Street, Cambridge, England (+44 1223 352500; www.fitzbillies.com). Dinner about £60 for two

Unforgettable food in an unlikely spot It's located in the shadow of a multiplex, but Alimentum is worth a detour from the scenic route. Under chef Mark Poynton, formerly of Midsummer House, it has gained a Michelin star for sensational food (smoked eel with apple, horseradish and truffle; pork belly, fillet and shoulder with black pudding and swede) at sensible prices. 152-154 Hills Road, Cambridge, England (+44 1223 413000; www.restaurantalimentum.co.uk). Three-course set menus from £24.50

There is no better place than Cambridge to buy books. Edge your way past piles of tattered Wisdens and the brilliant poetry section at the front of David's (16 St Edward's Passage; +44 1223 354619) to the antiquarian room, where fiercely competitive bibliophiles pop in three or four times a day for fear of missing the latest consignment. You can pick up a signed Laurie Lee paperback for £25 or lust after a Second Folio Shakespeare at £50,000. Good quality, poster-sized reproductions of William Blake's colour engravings are two for a tenner.

Independent shops are seeded sparsely through the high-street chains. At The Cambridge Satchel Company (17 Rose Crescent; +44 1223 366106), Japanese visitors practically weep with excitement at seasonal collections in shades of fondant or fluoro, hand embossed while you wait.

Ark (2 St Mary's Passage; +44 1223 363372) is the place for unusual gifts sourced from all over the world. Stylishly eccentric stock ranges from flavoured Italian toothpaste to jewelled dragonflies, wooden shoe-lasts and exquisite children's gardening gloves. If items start to appear in other shops, they immediately join the rolling sale on the upper floor.

Unlike Oxford, where town and gown each hold their own, Cambridge is basically a university on connecting streets. Most of the 31 colleges are fairly relaxed about visitors, although restrictions apply at exam times and in May Week (mid-June). You can generally slip past the porter's lodge with a look of scholarly intent. Step on the grass, however, and all hell will break loose (lawns are reserved for Fellows, a tradition pursued with heart-bursting zeal).

Each college has its distinct character. Jesus has a fine collection of contemporary sculpture, and the Fellows Garden of Clare is stunning. The big show-stopper colleges (King's, Trinity, St John's) offer official tours for a fee, well worth it if you are interested in their history. In Trinity's Wren Library, you can pore over Milton's poems in his own handwriting and the original manuscript of Winnie-the-Pooh. King's College Chapel, where Oliver Cromwell drilled the New Model Army on rainy days, is a world-class wonder. By far the nicest way to enjoy its fantastic detail - spun-sugar vaulting raised on columns slender as reeds - is to attend choral evensong (Monday-Saturday 5.30pm, Sunday 3.30pm; admission free). The answering rhythms of voices and stone are a glory not soon forgotten.

CAMBRIDGE HAS TALENT

The student-run ADC Theatre (Park Street; www.adctheatre.com) is the home of the Footlights comedy troupe, which launched John Cleese, Stephen Fry, Emma Thompson et al. Catch comedians before they're famous (and sometimes before they're funny) at the fortnightly Footlights Smokers.

The Faculty of Music's West Road Concert Hall (11 West Road; www.westroad.org) offers classical programmes of an international standard (and at sub-London prices), and colleges present year-round student drama and music events. Check out posters on the railings around All Saints Garden on Trinity Street.

The university has nine museums, most of which are free, making them ideal for a quick dip. Here are three of the best.

Kettle's Yard (Castle Street; www.kettlesyard.co.uk) was, until 1973, the home of Jim Ede, a former curator of London's Tate Gallery. His collection of 20th-century painting and sculpture by artists such as Ben and Winifred Nicholson, Alfred Wallis, Christopher Wood and Barbara Hepworth (many of them friends of Ede and his wife) is arranged with great warmth and a fabulous eye for placement in a light-filled domestic interior. You pop in for 10 minutes (from the outside, it looks tiny) and two hours later you're still there, wondering what it is about these objects in these relationships to one another that promotes such an extraordinary feeling of well-being.

The Scott Polar Research Institute (Lensfield Road; www.spri.cam.ac.uk/museum) has a small but beautifully assembled collection of artefacts, maps, photographs and documents relating to Arctic and Antarctic exploration. The very young will love dressing up in polar kit, and grown-ups will find themselves swallowing hard at the last letters home from Scott and his insanely heroic team.

There's a Harry Potter-ish feel to the sweetly Edwardian Sedgwick Museum of Earth Sciences (Downing Street; www.sedgwickmuseum.org). The skeleton of a giant elk is mounted on a plan chest full of rock samples, as though it had jumped up there and didn't know how to get down. Fossils are laid out with exquisite hand-lettered labels, and there is a collection of rocks collected by Darwin during the voyage of HMS Beagle. Erudite staff are delighted to chat with young visitors, and, best of all, the gift shop sells genuine 40-million-year-old fossilised turtle poo at two quid a throw, so the souvenirs are sorted!

Do not be fooled by the fantasy. Punting - the actual business with the pole - is fun for exactly seven minutes. Unless you're experienced, or immune to the shame of bashing about in a 24ft water-dodgem, it's a lot nicer to be punted.

Scudamore's (www.scudamores.com), the oldest punt-hire company in Cambridge, offers a chauffeur service (and they'll generally let you have a go if the river's not too busy). There are ghost and fireworks tours in May Week, and the company has recently launched a bat safari, hugely popular with kids. Everyone gets their own sonar detector, and an expert from the Wildlife Trust explains why there's nothing to be scared of as black shapes streak, like stealth bombers, through the river dusk.

For self-punters, the less crowded upper river is a better bet than the College Backs (where, to be honest, you get pretty much the same views on foot). From the Silver Street mooring, you can punt, row or kayak through the water-meadows to Grantchester. Kingfishers flash blue fire among the willows and it all looks like a Waterhouse painting (if Ophelia were to come floating by, you wouldn't be surprised).

You can pole through lilies to Byron's Pool, where the original Hooray swam during his time at Trinity. (Virginia Woolf also swam naked here with Rupert Brooke and was cross when her friends weren't shocked.) The Old Vicarage at Grantchester, made famous by Brooke's poem, is now owned by Jeffrey Archer, but there is honey still for tea at The Orchard (45-47 Mill Way, Grantchester; +44 1223 551125). Lunchtime queues at this historic tearoom stretch to infinity, but in the morning or late afternoon you can usually find a table (or, if it's sunny, a deckchair in a shady spot under the apple trees).